1. Modeling a flexible Detector Response Function in small animal SPECT using Geant4
Z. El Bitar1, R. H. Huesman2, R. Buchko2, D. Brasse1, G. T. Gullberg2
Université de Strasbourg, IPHC, 23 rue du loess, Strasbourg, France
Lawrence Berkeley National Laboratory, Berkeley California 94720, USA
Droite Workshop, Lyon, October 25, 2012

2. Outline Context Fully 3D image reconstruction
Monte Carlo modelling of the system matrix
Including geometrical misalignment
Correcting for penetration
Phantom and preclinical results

3. Single Photon Emission Computed Tomography
1- Injection of a radiotracer
2- Isotropic emission of gamma rays
3- Collimation: Filtering the directions of the photons
Parallel
Pinhole
Parallel
Pinhole

4. Fully 3D image reconstructionj
Projection p
Activity
distribution f
detector i
Discrete formulation of the image reconstruction problem
p = R x f
R(i,j) : Probability that a photon emitted in a voxel i to ba detected in a pixel j
Simultaneous reconstruction of the whole volume
Taken into account of 3D physcial phenomena such as : scatter and detector response
Solving p = R f using an iterative method like MLEM, OSEM, ART, GC.

5. Données fonctionnelles TEMP (fusion avec TDM)
Modélisation Monte Carlo de R
Modèle du TEMP 2 1
densité
composition atomique
Coupe voxellisée (obtenue par TDM) j
Modélisation Monte-Carlo des probabilités qu’un photon émis en voxel i soit détecté en pixel j i
détecteur 3
mesuresTEMP P 4
Estimation de R
11’
Revoir le discours sur le transparent – fonte de R dans la case 3
Mettre des animations adaptées pour faire arriver les différentes étapes. 5
Résolution du problème inverse P = Rx f
dans un algorithme itératif
(ML-EM, OSEM, ART, CG …)
Données fonctionnelles TEMP (fusion avec TDM)

6. What’s the problem in small animal SPECT ?
Monte Carlo simulations are time consuming.
Detection efficiency is very low in small animal SPECT due to pinhole collimation.
Pinhole SPECT modality is very sensitive to geometrical misalignments => a system matrix should be computed for each set up.
We must find a solution to avoid resimulation by Monte Carlo methods for each exam => need to have a detector model independent of the acquisition set up.

7. Decomposition of the system matrix
R = Rsubject + Rdetector
To be computed for each subject/exam
Computed once-for-all

8. Definition of a family of lines (or directions)
pixel j
collimator
crystal
bin i
The family of lines Lij is defined by all photons’ directions entering the collimator
at bin i and aiming the crystal’s pixel j => Calculation of the Detector Response
function table (DRFT).

9. SPECT Components Rectangular knife edge collimator
Aperture : 2 x 1.5 mm2
Rectangular knife edge collimator
Aperture : 0.6 x 0.4 mm2
Both collimators
Shielding
SPECT : General Electric – Hawkeye 3

10. Collimator + shielding Collimator + Shielding + Crystal
SPECT model in Geant4
Collimator + shielding
Collimator
Collimator + Shielding + Crystal

11. Profiles drawn on the projections of three point sources located at :
Validation of the DRFT
Profiles drawn on the projections of three point sources located at :
(-20 mm, 0, 0), (0, 0, 0) and (20 mm, 0, 0).
Speed up by a factor of 74

12. Pinhole acquisition geometry
7 parameters to estimate:
m : mechanical shift
electronic shift : eu , ev
distance collimator to centre of rotation : r
distance collimator to crystal : f
Tilt and Twist angle: Ф, Ψ
Calibration parameters are estimated by minimizing the following functions :

13. Calibration phantom 1 2 3

14. Geometrical Parameters Estimation
u (head1)
v (head1)
u (head2)
v (head2) 1 v 2 3 u

15. Trajectories' fit
Head1
Head2

16. Reconstructed Images of a sphere (Ø = 2 mm).
Mechanical shift y
crystal s
shift m
shift m
collimator x
Reconstructed Images of a sphere (Ø = 2 mm).
Original
m = 2 mm
Corrected z

17. What’s the point ?
After performing Monte Carlo simulations and calculating a Detector Response Function Table, one is home-free to used the DRFT(~500 Mbytes).
The DRFT can incorporate with ease for any geometrical misalignments (translation, rotation): all what is required is the equation of the entry plan (collimator) and the detection plan (crystal).
Resimulation of all photons’ trajectories inside the detector is not required for each study.

18. Target emission window:x z y
Target emission window:
{x > -1; x < 1}
{z > -1; z < 1}
{x > -3; x < 3}
{z > -3; z < 3}
{x > -3; x < -1} U { x > 1; x < 3 }
{z > -3; z < -1} U { z > 1; z < 3 }
Target window = 2 mm
Target window = 6 mm
Penetration window

19. Penetration validationx d α
*Roberto Accorsi and Scott Metzler : Analytic Determination of the Resolution-equivalent effective diameter of a Pinhole Collimator (IEEE, TMI, vol 23, June 2004)

20. Penetration effect : simulation study
Projection of Cylindre : Diameter = 40 mm, Height = 40mm
Penetration window
Target window = 2 mm
Target window = 6 mm

21. Tomography Spatial resolution: Where:
Rint is the intrinsic spatial resolution of the crystal
Rgeo is the spatial resolution due to the geometry of the pinhole
M is the magnification factor (distante detector-pinhole)/(distance pinhole-centerFOV)
Where:
d is the diameter of the aperture of the pinhole
Expected radial spatial resolution with:
Wide collimator (2 x1.5 mm2) : 2.55 mm
Narrow collimator (0.6 x 0.4 mm2) : 1.14 mm

22. Effect on reconstruction
Window projection : 2 mm
Window system matrix : 2 mm
Window projection : 2 mm
Window system matrix : 6 mm
Window projection : 6 mm
Window system matrix : 2 mm
Window projection : 6 mm
Window system matrix : 6 mm

23. Real data: micro Jaszczack phantom (1)
4.8 mm
4.0 mm
3.2 mm
2.4 mm
1.2 mm
1.6 mm

24. Real data: micro Jaszczack phantom (2)
2 mm
1.5 mm
Correction for the penetration effect
Window system matrix : 2 mm
Window system matrix : 6 mm

25. Real data: micro Jaszczack phantom (3)
0.6 mm
0.4 mm
Misalignment correction
Before correction
After correction

26. Computation time : parallelization of the system matrix calculation
Each processor calculate the system
matrix corresponding to a slice
Computation time for an object of
152x152x152 voxels ~= 20 minutes
Field of view

27. Parallelization of the iterative reconstruction
Reconstruction Tomographique
Slaves tasks:
Master
PC 1
PC 2
PC 10
Slave
Forward-projection
2/3
Send projections
Receive projections
Receive CC
Send the CC to the slaves
6/7
Volume’s slices
to be reconstructed
Back-projection
Master Tasks
Sum the projections
Compute the correction coefficients
(CC = Pmeasured/ Pestimated)

28. Most recent result 150x150x150 voxels (0. 4x0. 4x0
Most recent result 150x150x150 voxels (0.4x0.4x0.4 mm3), 90 projections (128x88 pixels) Size of system matrix ~= 40 GBytes MLEM (50 iterations) < 3 minutes
0.6 x 0.4 mm2

29. Small animal result Reconstruction slice of a rat heart using MIBG
(ML-EM, 50 iterations)
Profile drawn through the heart
El Bitar et al, submitted to Phys Med Biol

30. Acknowledgment Grant T Gullberg (discussion)
Ronald H Huesman (discussion)
Rostystalv Boutchko (calibration)
Archontis Giannakdis (discussion)
Martin Boswell (computing)
Nichlas Vandeheye (experiments)
Steven Hanrahan (experiments)
Bill Moses (experiments)
Special thanks to the Franco-American Fulbright-commission !